Some theorems on planar mappings

Abstract

A mapping is called planar if for every nonzero the difference mapping D f,a : x → f(x∈+∈a)∈-∈f(x) is a permutation of . In this note we prove that two planar functions are CCZ-equivalent exactly when they are EA-equivalent. We give a sharp lower bound on the size of the image set of a planar function. Further we observe that all currently known main examples of planar functions have image sets of that minimal size. © 2008 Springer-Verlag Berlin Heidelberg.